9^2(13^2 + 14^2 + 15^2) black coins, i x j coins in a_{ij} in a 27x27 board
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 3.2
September 23, 2021
combinatoricsalgebra
Problem Statement
In a video game, there is a board divided into squares, with rows and columns.
The squares are painted alternately in black, gray and white as follows:
in the first row, the first square is black, the next is gray, the next is white, the next is black, and so on;
in the second row, the first is white, the next is black, the next is gray, the next is white, and so on;
in the third row, the order would be gray-white-black-gray and so on;
the fourth row is painted the same as the first, the fifth the same as the second,
the sixth the same as the third, and so on.
In the box in row and column , there are coins.
For example, in the box in row and column there are coins.
Verify that in total there are, in the black squares, coins.